## Illinois Journal of Mathematics

### Minimal Lagrangian submanifolds in indefinite complex space

Henri Anciaux

#### Abstract

Consider the complex linear space endowed with the canonical pseudo-Hermitian form of arbitrary signature. This yields both a pseudo-Riemannian and a symplectic structure. We prove that those submanifolds which are both Lagrangian and minimal with respect to these structures minimize the volume in their Lagrangian homology class. We also describe several families of minimal Lagrangian submanifolds. In particular, we characterize the minimal Lagrangian surfaces in pseudo-Euclidean complex plane endowed with its natural neutral metric and the equivariant minimal Lagrangian submanifolds of indefinite complex space with arbitrary signature.

#### Article information

Source
Illinois J. Math., Volume 56, Number 4 (2012), 1331-1343.

Dates
First available in Project Euclid: 6 May 2014

https://projecteuclid.org/euclid.ijm/1399395835

Digital Object Identifier
doi:10.1215/ijm/1399395835

Mathematical Reviews number (MathSciNet)
MR3231486

Zentralblatt MATH identifier
1290.53074

#### Citation

Anciaux, Henri. Minimal Lagrangian submanifolds in indefinite complex space. Illinois J. Math. 56 (2012), no. 4, 1331--1343. doi:10.1215/ijm/1399395835. https://projecteuclid.org/euclid.ijm/1399395835

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